# QCD evolution of the orbital angular momentum of quarks and gluons: Genuine twist-three part

## TL;DR

This paper numerically solves the one-loop QCD evolution equations for the genuine twist-three orbital angular momentum distributions of quarks and gluons, enhancing understanding of their scale dependence in polarized nucleons.

## Contribution

It provides the first numerical solution for the evolution of genuine twist-three OAM distributions and explores the scale dependence of potential angular momentum.

## Key findings

- Evolution of twist-three OAM distributions is identical to Efremov-Teryaev-Qiu-Sterman function.
- The evolution of OAM distributions is now well-understood when combined with Wandzura-Wilczek parts.
- First analysis of the scale dependence of potential angular momentum.

## Abstract

We present the numerical solution of the one-loop QCD evolution equation for the genuine twist-three part of the orbital angular momentum (OAM) distributions of quarks and gluons inside a longitudinally polarized nucleon. This is based on the observation that the evolution is identical to that of the Efremov-Teryaev-Qiu-Sterman function for transverse single spin asymmetry. Together with the known evolution of the Wandzura-Wilczek part, the one-loop evolution of OAM distributions is now practically under control. We also study, for the first time, the scale dependence of the potential angular momentum defined as the difference between the Ji and Jaffe-Manohar definitions of OAM.